On the numerical resolution of the second-order viscoacoustic and viscoelastic anisotropic wave equations using the recursive convolution method

Accurate and efficient seismic wave modeling is fundamental for the high-resolution seismic full-waveform inversion and correct interpretation of seismic data. Based on the viscoelastic mechanism of the Generalized Standard Linear Solid and the constitutive relationship between stress and strain, we demonstrate a generalized recursive formula using the Taylor series expansion to directly compute the temporal convolution in the constitutive equation, rather than solving auxiliary differential equations of the memory variables in the conventional method. New sets of the second order viscoacoustic and viscoelastic anisotropic wave equations are established with the new recursive temporal convolutions, which completely replaces the traditional auxiliary differential equations of the memory variables. The error analysis shows the proposed method can offer better accuracy than the existing recursive methods, and is very competitive with the widely used memory variable method. The numerical results comparing the different methods show the accuracy and feasibility of the generalized recursive convolution method to simulate the viscoacoustic and viscoelastic anisotropic waves.